Fine Selmer torsion conjecture for Hida deformations

Retain the Hida-family settings of the source. Let $\mathcal{A}$ be the big Galois representation, let $F_\infty$ be a $\mathbb{Z}_{p}$-extension of a number field $F$, and write $\Gamma=\operatorname{Gal}(F_\infty/F)$. Let $Y(\mathcal{A}/F_\infty)$ be the Pontryagin dual of the fine Selmer group of $\mathcal{A}$. Hida-deformation fine Selmer torsion conjecture. The module $Y(\mathcal{A}/F_\infty)$ is torsion over

$$\mathcal{R}[[\Gamma]].$$

This conjecture extends the fine Selmer torsion prediction to a Hida deformation and would organize the torsionness of its arithmetic specializations. The paper notes that even finite generation over the Hida coefficient ring is not known in general, so the conjecture remains open.